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Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What

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Bunuel
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Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink] New post  15 Mar 2015, 23:06
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Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What is the value of Q?

A. 3
B. 3 1/7
C. 3 2/7
D. 3 3/7
E. 3 1/2

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Lucky2783
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Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink] New post  22 Mar 2015, 09:44
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Bunuel wrote:
Attachment:
ppocg_img3.png
Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What is the value of Q?

A. 3
B. 3 1/7
C. 3 2/7
D. 3 3/7
E. 3 1/2

Kudos for a correct solution.




Oops , i am missing a chance to earn a easy kudo .
here we go ,
Slope of line when calculated with (-5,-1) (2,2) = \(3/7\)
Slope of line when calculated with (2,2) (5,q) = \(\frac{q-2}{5-2}\)
\(\frac{q-2}{3} = \frac{3}{7}\)
\(q= 3 \frac{2}{7}\)
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KarishmaB
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Line J passes through the points ( 5, 1), (2, 2), and (5, Q). What [#permalink] New post  Updated on: 09 Aug 2023, 03:19
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Bunuel wrote:
Attachment:
ppocg_img3.png
Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What is the value of Q?

A. 3
B. 3 1/7
C. 3 2/7
D. 3 3/7
E. 3 1/2

Kudos for a correct solution.


I am surprised no one has solved this question yet!

Using the slope concept, if x co-ordinate increases by 7 (from (– 5, – 1) to (2, 2)), y co-ordinate increases by 3 (from -1 to 2). So when x co-ordinate increases by further 3 (from 2 to 5), the y co-ordinate will increase by (3/7)*3 = 9/7 = 1 (2/7)
So y co-ordinate will become 2 + 1(2/7) = 3 (2/7)
Answer (C)

Here is a post on the slope concept: https://anaprep.com/geometry-using-slop ... fectively/
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Originally posted by KarishmaB on 16 Mar 2015, 22:09.
Last edited by KarishmaB on 09 Aug 2023, 03:19, edited 1 time in total.
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Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink] New post  17 Mar 2015, 09:50
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Here is my approach:

m= 2+1 / 2+5 = 3/7

y = (3/7)x + b
2 = (3/7)2 + b
b = 8/7

y = (3/7)5 + (8/7)
y = 23/7 = 3 2/7

Answer: C
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Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink] New post  22 Mar 2015, 12:04
C


slopes are same for all the points

so we can equate the slope3/7 to the one with Q co-ordianare

getting 23/7
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Bunuel
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Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink] New post  23 Mar 2015, 05:33
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Bunuel wrote:

Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What is the value of Q?

A. 3
B. 3 1/7
C. 3 2/7
D. 3 3/7
E. 3 1/2

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

Think about this visually. From (–5, –1) to (2, 2), the line moves right 7 and up 3, so that’s a slope of 3/7.

From the point (2, 2) to the point (5, Q), there’s a horizontal distance of 3, an unknown vertical distance — call it h, so that h = Q – 2, or Q = h + 2. The ratio of this vertical and horizontal distance must equal the slope.

h/3 = 3/7 --> h = 9/7.

That’s h. Now, add 2 to get Q.

Q = h + 2 = 3 2/7.

Answer = (C)
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Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink] New post  13 May 2015, 10:10
Let the 3 points be A(-5, -1) B(2, 2) and C(5, Q).

Equation of line passing through A and B is :
(y-y1) = M(x-x1)
y + 1 = 3/7( x + 5) .. here slope(M) is calculated as : y2 - y1/x2 -x1( gives 3/7)

Since point C(5, Q) passes through the line, so it should satisfy the above equation.
Q + 1 = 3/7 (5 + 5)
Q = 30/7 - 1
Q = 23/7 or 3 2/7

Option C
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Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink] New post  25 Feb 2017, 06:54
As slope for the line remains constant, slope between (-5,-1) and (2,2) would be the same.
thus, {2- (-1)}/{2-(-5)} = (Q-2)/(5-2)
=> 3/7=(Q-2)/3
=> Q-2=9/7 => Q=23/7 = 3 2/7
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KarishmaB
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Line J passes through the points ( 5, 1), (2, 2), and (5, Q). What [#permalink] New post  Updated on: 09 Aug 2023, 03:18
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VeritasPrepKarishma wrote:
Bunuel wrote:
Attachment:
ppocg_img3.png
Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What is the value of Q?

A. 3
B. 3 1/7
C. 3 2/7
D. 3 3/7
E. 3 1/2

Kudos for a correct solution.


I am surprised no one has solved this question yet!

Using the slope concept, if x co-ordinate increases by 7 (from (– 5, – 1) to (2, 2)), y co-ordinate increases by 3 (from -1 to 2). So when x co-ordinate increases by further 3 (from 2 to 5), the y co-ordinate will increase by (3/7)*3 = 9/7 = 1 (2/7)
So y co-ordinate will become 2 + 1(2/7) = 3 (2/7)
Answer (C)



Responding to a pm:

Quote:

I really did not understand how did u get 2 ahead of 9/7.
Also, the concept of slopes that you used, can u explain it to me. I do understand that slopes is rise/ run. or I have read it in school as Tan angle that line makes with x -axis. Now, the approach you used I drew inference that Slope is with an increase in an x coordinate the y coordinate increases with according to slope .


If you write \(\frac{9}{7}\) in mixed fractions, you get \(1\frac{2}{7}\).

As for the slope concept, I have explained it in detail in this blog post: https://anaprep.com/geometry-using-slop ... fectively/
Take a look and get back to me if any doubts remain.
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Originally posted by KarishmaB on 10 Apr 2017, 00:38.
Last edited by KarishmaB on 09 Aug 2023, 03:18, edited 1 time in total.
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Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink] New post  01 Apr 2020, 15:11
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Bunuel wrote:
Attachment:
ppocg_img3.png
Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What is the value of Q?

A. 3
B. 3 1/7
C. 3 2/7
D. 3 3/7
E. 3 1/2

Kudos for a correct solution.


Since the slope of the line has to be the same no matter which pair of points we use to determine the slope, we can create the equation:

(2 - (-1)) / (2 - (-5)) = (Q - 2) / (5 - 2)

Notice that on the left hand side of the equation, we use the points (2, 2) and (-5, -1) to determine the slope and on the right hand side, we use the points (5, Q) and (2, 2) to do so. Now, solving the equation, we have:

3/7 = (Q - 2)/3

7(Q - 2) = 3(3)

7Q - 14 = 9

7Q = 23

Q = 23/7 = 3 2/7

Answer: C
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Re: Line J passes through the points ( 5, 1), (2, 2), and (5, Q). What [#permalink] New post  10 Apr 2023, 05:59
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